Consider the function g. 9(-) = 6() For the x-values given in the table below, determine the corresponding values of g(x) and plot each point on the graph.. -1 0 1 2 g(x) Drawing Tools Click on a tool to begin drawing * Delete Undo Reset Select Point 14 13 12 11 10 9 00 reserved.
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we have the function
[tex]g(x)=6(\frac{3}{2})^x[/tex]Find out the value of function g(x) for each value of x
so
For x=-1
substitute the value of x in the function g(x)
[tex]\begin{gathered} g(-1)=6(\frac{3}{2})^{-1} \\ g(-1)=6(\frac{2}{3}) \\ g(-1)=4 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} g(0)=6(\frac{3}{2})^0 \\ g(0)=6 \end{gathered}[/tex]For x=1
[tex]\begin{gathered} g(1)=6(\frac{3}{2})^1 \\ g(1)=9 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} g(2)=6(\frac{3}{2})^2 \\ g(2)=13.5 \end{gathered}[/tex]using a graphing tool
plot the different points
so
we have
(-1,4)
(0,6)
(1,9)
(2,13.5)
see the attached figure to better understand the problem
please wait a minute
Related Questions
A family is driving home from Georgia. The graph shows the distance away 1 point from home, in miles, as a function of time, in hours. Use the graph to estimate the average rate of change from t=0 to t=7.2. **Round answer to 1 decimal place. ***
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Basically we need to find the slope:
[tex]\begin{gathered} avg=\frac{f(b)-f(a)}{b-a} \\ \text{Where:} \\ a=0 \\ b=7.2 \\ f(a)=420 \\ f(b)=0 \\ avg=\frac{0-420}{7.2-0}=\frac{-420}{7.2}=-\frac{175}{3}\approx-58.33 \end{gathered}[/tex]You poured 1/4 of the juice from a 2-liter bottle while serving guests at a party. How much juice, in liters, is still left in the bottle?
How much juice was used?
How much is left?
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Answer:
1.5 litters is left and 0.5 litters was used
Step-by-step explanation:
2 litters divided by 4 = 0.5 litters and you can do the rest of the math if needed
I need to know the answer to this question please
Answers
Answer:
Explanation:
Given:
[tex]3)\text{ }(32\div16)\div4\text{ = 32 }\div\text{ \lparen16}\div4)[/tex]To find:
the property demonstrated in the equation
Associative property is in the form:
(a + b) + c = a + (b + c)
The left side = right side
[tex]\begin{gathered} (32\div16)\div4\text{ = 32 }\div\text{ \lparen16}\div4) \\ Associative\text{ property was applied but the left side is not equal to the right side} \end{gathered}[/tex]That is why associative priperty is used for addition and multiplication
Two systems of equations are given below.For each system, choose the best description of its solution.If applicable, give the solution.System AThe system has no solution.The system has a unique solution:3x + 5y = 112x + 5y=4(x, y) = (1,5The system has infinitely many solutions.System BThe system has no solution.The system has a unique solution:y = 3x + 7y = 3x + 4(x, y) = (2, 2)The system has infinitely many solutions.
Answers
We are given the following system of equations:
[tex]\begin{gathered} 3x+5y=11,(1) \\ 2x+5y=4,(2) \end{gathered}[/tex]We can solve this system of equations using the method of elimination. To do that we will multiply equation (2) by -1:
[tex]-2x-5y=-4,(3)[/tex]Now we add equations (1) and (3):
[tex]3x+5y-2x-5y=11-4[/tex]Adding like terms:
[tex]x=7[/tex]Now we replace the value of "x" is equation (1):
[tex]\begin{gathered} 3(7)+5y=11 \\ 21+5y=11 \end{gathered}[/tex]Now we subtract 21 to both sides:
[tex]\begin{gathered} 5y=11-21 \\ 5y=-10 \end{gathered}[/tex]Dividing both sides by 5:
[tex]\begin{gathered} y=-\frac{10}{5} \\ y=-2 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex](x,y)=(7,-2)[/tex]For the second system of equations:
[tex]\begin{gathered} y=3x+7,(1) \\ y=3x+4,(2) \end{gathered}[/tex]These equations represent two lines with the same slope, and therefore, parallel lines. Since they are parallel lines this means that the system has no solutions.
About 1% of the population has a particular genetic mutation. 100 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 100. (Remeber that standard deviation should be rounded to one more decimal place than the raw data, in this case 1 decimal place is necessary.)
Answers
ANSWER:
1.0
STEP-BY-STEP EXPLANATION:
Given:
p = 1% = 0.01
q = 1 - p = 1 - 0.01 = 0.99
n = 100
The standard deviation is calculated using the following formula:
[tex]\begin{gathered} \sigma=\sqrt{n\cdot p\cdot q} \\ \\ \text{ We replace each value and obtain the standard deviation:} \\ \\ \sigma=\sqrt{100\cdot0.01\cdot0.99} \\ \\ \sigma=\sqrt{0.99} \\ \\ \sigma=0.99498 \\ \\ \sigma=0.995\rightarrow1\text{ decimal place}\rightarrow1.0 \end{gathered}[/tex]Therefore, the standard deviation is equal to 1.0
Order the angles of the triangle from smallest to biggest T R 12 addre S
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It's important to know that each side is related to its angle in front. In other words, the greatest side has the greatest angle in front, and so on.
Having said that, the order of the angles from least to greatest is
[tex]\begin{gathered} 6<11<12 \\ \angle S<\angle R<\angle T \end{gathered}[/tex]Therefore, the order is S, R, and T.Write inequalities to represent the situation below.Latoya exercises no less than 50 minutes per day.Use t to represent Latoya's amount of exercise (in minutes per day).(Thank you for the help!)
Answers
To answer this question, we have that:
1. Latoya exercises no less than 50 minutes per day.
In this case, we can say that Latoya exercises more than 50 minutes per day.
Therefore, if we have that t represents Latoya's amount of exercise - in minutes per day, we can express this using inequality as follows:
[tex]t>50[/tex]In summary, we can represent the situation as:
[tex]t>50[/tex]use the given actual and magnified lengths to determine which of the following insects were looked at using the same magnifying glass (with the same scale factor)
Answers
Grasshoper
Actual: 2 in
Magnified: 15 in
The scale factor is given by:
[tex]k=\frac{15}{2}=7.5[/tex]Black beetle
Actual: 0.6 in
Magnified: 4.2 in
The scale factor is:
[tex]k=\frac{4.2}{0.6}=7[/tex]Honybee
Actual: 5/8 in
Magnified: 75/16 in
The scale factor is:
[tex]k=\frac{\frac{75}{16}}{\frac{5}{8}}=\frac{75\cdot8}{16\cdot5}=\frac{600}{80}=\frac{15}{2}=7.5[/tex]Monarch butterfly
Actual: 3.9 in
Magnified: 29.25 in
The scale factor is:
[tex]k=\frac{29.25}{3.9}=\frac{15}{2}=7.5[/tex]Answer:
Grasshoper, Honybee and Monarch butterfly have the same factor scale = 7.5
Black beetle has a factor scale = 7
Express the following ratio in simplest form 39:10
Answers
ok
If we have
[tex]\text{ }\frac{39}{10}[/tex]It was not possible to simplify it anymore so the answer will be the same.
It is not possible to implify it because the are no common fators between 39 and |0.
Part 2 out of 2If you plan to cancel your internet service after 11 months, which is the cheaper option
Answers
m = number of months
Option 1 cost = 35 + 20m
Option 2 cost = 25m
Part 1: If the cost is equal for both otpions, then we can write: 35 + 20m = 25m, solving for m:
5m = 35 ==> m = 35/5 = 7
m = 7
In month 7, the cost is 35 + 20(7) = 35 + 140 = 175
Part 2:
Option1 cost when m = 11: 35 + 20(11) = 35 + 220 = 255
Option2 cost when m = 11: 25(11) = 275
Option 2 costs more than option 1, so Option 1 is cheaper
Find the coordinates of the centroid.F(1,5) G(-2,7) H(-6,3)
Answers
The coordinates of the centroid is
[tex](-\frac{7}{3},5)[/tex]Explanation:The coordinates of the centroid of a triangle is given as:
[tex](\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]Using the above formula, we have:
[tex]\begin{gathered} C=(\frac{1+(-2)+(-6)}{3},\frac{5+7+3}{3}) \\ \\ =(-\frac{7}{3},\frac{15}{3}) \\ \\ =(-\frac{7}{3},5) \end{gathered}[/tex]The ratio of the quantities of sugar and flour needed to bake a cake is 2:5. What is the quantity of sugar needed for a cake, if 750 grams of flour are used to bake it?
Answers
The quantity of sugar needed for a cake, if 750 grams of flour are used to bake it is 300 grams.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
In this case, the ratio of the quantities of sugar and flour needed to bake a cake is 2:5.
The quantity of sugar needed is illustrated by x.
This will be:
2/5 = x/750
Cross multiply
5x = 2 × 750
5x = 1500
Divide
x = 1500/5
x = 300
The sugar needed is 300 grams.
Learn more about ratio on:
brainly.com/question/2328454
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Which of the following expressions can be used to rationalize the fractions below?
Answers
SOLUTION:
Case: Rationalizing fractions
Method:
[tex]\begin{gathered} \frac{16}{\sqrt{2}} \\ \Rightarrow \\ \frac{16}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\ =\frac{16\sqrt{2}}{\sqrt{4}} \\ =\frac{16\sqrt{2}}{2} \\ =8\sqrt{2} \end{gathered}[/tex]Final answer: Option (A)
[tex]\frac{\sqrt{2}}{\sqrt{2}}[/tex]Tell which choice, 100, 500, or 1,000, is the best estimate of the solution.39.4x = 37,627a. 1,000b.500c.100Please select the best answer from the choices providedΑВС
Answers
39.4 x = 37627
Divide both sides by 39.4
[tex]\begin{gathered} \frac{39.4x}{39.4}=\frac{37627}{39.4} \\ x=955 \end{gathered}[/tex]955 is nearest to 1000 than 500 or 100
Then the best estimate is 1000
The answer is A
17. A publisher marks up a textbook by 60%, and a bookstore further marks up the textbook by 25%. What percentage of the original cost do you pay?%
Answers
A publisher marks up a textbook by 60%, and a bookstore further marks up the textbook by 25%. What percentage of the original cost do you pay?
Let
x ------> original cost
so
1) publisher marks up a textbook by 60%
cost=1.60x
2) bookstore further marks up the textbook by 25%
cost=1.60x(1.25)=2x
therefore
200%The lenath of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of .7 minutes. What is the probability that a conversation lasts longer than 6 minutes?
Answers
To solve this problem we can use a z-table. First, we convert our score to a z-score using the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where mu represents the mean and sigma represents the standard deviation.
Using this formula in our problem, we have:
[tex]z=\frac{6-5}{0.7}=\frac{10}{7}\approx1.429[/tex]This z-score represents the position where the phone call is equal to 6 minutes. On a z-table, we're going to find the area between the mean and this z-score, since we want the probability that a conversation lasts longer than 6 minutes, we want the area above it. To calculate this area, we're going to subtract the value given on the z-table from 0.5.
The value on the z-table is:
Then, our probability is:
[tex]P(x>6)=0.5-0.4236\approx0.077[/tex]The answer is 0.077.
an unusually shaped section of a park is to be paved. this section is drawn to scale below. the length of a single grid segment is 1 m.
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Since the length of a single grid square is 1m, then its area is:
[tex]A=1m\times1m=1m^2\text{.}[/tex]Now, to compute the area of the given section we will use the following diagram.
To compute the area of each triangle we will use the following formula for the area of a triangle:
[tex]\begin{gathered} A=\frac{bh}{2}, \\ \text{where b is the base of the triangle and h is its height.} \end{gathered}[/tex]And to compute the area of the rectangle we will use the following formula:
[tex]\begin{gathered} A=bh, \\ \text{where b is the base of the rectangle and h is its height.} \end{gathered}[/tex]Therefore the area of triangle A is:
[tex]A_A=\frac{6m\cdot2m}{2}=6m^2\text{.}[/tex]The area of triangle B is:
[tex]A_B=\frac{4m\cdot2m}{2}=4m^2\text{.}[/tex]The area of triangle C is:
[tex]A_C=\frac{3m\cdot1m}{2}=1.5m^2\text{.}[/tex]The area of triangle D is:
[tex]A_D=\frac{5m\cdot1m}{2}=2.5m^2\text{.}[/tex]The area of rectangle E is:
[tex]A_E=12m^2\text{.}[/tex]Finally, the area of the given section is:
[tex]\begin{gathered} A=A_A+A_B+A_C+A_D+A_E \\ =6m^2+4m^2+1.5m^2+2.5m^2+12m^2=26m^2\text{.} \end{gathered}[/tex]Answer:
The area of a single grid square is:
[tex]1m^2\text{.}[/tex]The approximate area of the section that will be paved is:
[tex]26m^2\text{.}[/tex]
What type of number is 4π?whole numberintegerrational numberirrational number
Answers
Answer:
(D)Irrational number
Explanation:
The number π is Irrational because the digits after the decimal point go on indefinitely.
Therefore, a product of a number and π is also an Irrational Number.
In ABC, AB = 10 and BC = 5. Which expression is always true?
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Using the Triangle inequality:
In every triangle the sum of the lengths of any two sides is always greater than the length of the remaining side, so:
[tex]\begin{gathered} AB+BC>AC \\ so\colon \\ 5what is the value of f(0)=
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SOLUTION:
Case:
Given:
Required:
Method:
Step 1:
Step 2:
Step 3:
Final answer:
Enter an equation for the function. Give your answer in the form a(6"). In theevent that a = 1, give your answer in the form b".A laser beam with an output of 4 milliwatts is directed into a series of mirrorsThe laser beam loses 6% of its power every time it reflects off of a mirror. Thepower p(n) is a function of the number n of reflections.The equation is p(n) = 0
Answers
From the data provided, we have the following;
Initial power output = 4 milliwatts
Power lost per reflection = 6% (OR 0.06)
We need to find a function that shows the power each time the laser beam is reflected off a mirror.
Note that the general equation for an exponential decay/loss is given as;
[tex]\begin{gathered} y=a(1-r)^x \\ OR \\ f(x)=a(1-r)^x \end{gathered}[/tex]Note also that (1 - r) is often replaced by b. Therefore, the equation can be written as;
[tex]\begin{gathered} f(x)=a(1-r)^x^{} \\ f(x)=ab^x \end{gathered}[/tex]Where the number of reflections is given by n and p(n) is a function of the number of reflections, we now have;
[tex]p(n)=ab^n[/tex]Where the variables are;
[tex]\begin{gathered} a=4\text{ milliwatts (initial value)} \\ r=0.06 \end{gathered}[/tex]We now have the function as;
[tex]\begin{gathered} p(n)=a(1-0.06)^n \\ p(n)=a(0.94)^n \end{gathered}[/tex]ANSWER:
[tex]p(n)=a(0.94)^n[/tex]The distance from Becca’s house to Liz’s house is 13 kilometers. Approximately how many miles does Becca live from Liz? Use the conversion factor shown below.
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Data:
13 km
Convert to miles
(1 km is equal to 0.6214 miles)
[tex]13\operatorname{km}\cdot\frac{0.6214mi}{1\operatorname{km}}=8.078mi[/tex](1 mile is equal to 1.6093km)
[tex]13\operatorname{km}\cdot\frac{1mi}{1.6093\operatorname{km}}=8.078mi[/tex]Then, Becca lives 8.078 miles (aprroximately 8.1 miles) from LizCampbells wants to try and sell their soup in boxes rather than cans. The originalcans have a height of 6 inches and a diameter of 4 inches. If the boxes can only be 2inches deep, 4 inches wide and the keep the volume the same, what is the height ofthe new rectangplar box?
Answers
Given
Original cans
Height of 6 inches
Diameter of 4 inches
New boxes
2 inches deep
4 inches wide
Same volume
Procedure
Now let's calculate the volume of the soup cans.
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(2)^2(6) \\ V=75.36\text{ cubic inches} \end{gathered}[/tex]Now let's calculate the volume of the boxes
[tex]\begin{gathered} V=2\cdot4\cdot h \\ V=8h \end{gathered}[/tex]Now we must equal the volume of the cans and then calculate the height.
[tex]\begin{gathered} 75.36=8h \\ h=\frac{75.36}{8} \\ h=9.42\text{ inches} \end{gathered}[/tex]The height of the boxes must be equal to 9.42 inches.
Please explain step by step on how to solve As I am brand new to this What is the median of 19,3,7,1,11,19,2,3,17,4,14,12
Answers
Answer:
The median is 9
Explanation:
The median of a data set is the value that lies in the middle of the ordered data set.
In this case, we have:
19,3,7,1,11,19,2,3,17,4,14,12
We need to order the list in ascending order:
1, 2, 3, 3, 4, 7, 11, 12, 14, 17, 19, 19
There are 12 values, since is an even number, the median is the average of the pair in the middle.
In this case, the pair in the middle is 7 and 11. The average is:
[tex]\frac{7+11}{2}=\frac{18}{2}=9[/tex]Thus, the median is 9
A. Substitute the x-values shown to the right into y = xand y = |x| to find several points on their graphs. Usethe probe to check your work.
Answers
For the function y=x we just have to replace the values in the table for the x so:
[tex]\begin{gathered} -3\to x=-3 \\ -2\to x=-2 \\ -1\to x=-1 \\ 0\to x=0 \\ 1\to x=1 \\ 2\to x=2 \\ 3\to x=3 \end{gathered}[/tex]and for y = |x| we have to change all the negative values for positive:
[tex]\begin{gathered} -3\to\mleft|x\mright|=3 \\ -2\to|x|=2 \\ -1\to|x|=1 \\ 0\to|x|=0 \\ 1\to|x|=1 \\ 2\to|x|=2 \\ 3\to|x|=3 \end{gathered}[/tex]Please help will mark brain list
Answers
answer:
y = -2/3x -4/3
step-by-step explanation:
you start with 6x-9y = 12. you need to get y alone and on its own side of the equal sign.
starting easy, all coefficients (6, -9, and 12) have a GCF of 3. so, let's divide all sides by 3.
you are left with 2x-3y=4. now, we need to get -3y on its own side of the equal sign before we can get rid of its coefficient (-3). also, when identifying the coefficient of x, y, or any variable, include the + or - sign. you just don't need to write +, but you have to write -.
2x-3y=4 means we subtract 2x from both signs because it is positive. we now have
-3y = 2x + 4. let's divide by -3 to get y on it's own
y = -2/3x -4/3
Which expression is equivalent to75a7b"40213,9 ? Assume a=1 and C=0.
Answers
we have the expression
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}[/tex]Remember that
[tex]\frac{75}{40}=\frac{15}{8}=\frac{15}{2^3}[/tex][tex]\frac{a^7}{a^{(13)}}=\frac{1}{a^6}[/tex]substitute
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}=\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}[/tex]we have that
[tex]2^3a^6c^9=(2a^2c^3)^3[/tex]substitute
[tex]\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}=\frac{\sqrt[3]{15b^4}}{(2a^2c^3)}=b\frac{\sqrt[3]{15b^{}}}{(2a^2c^3)}[/tex]answer is the second optionyou have the numbers 1-24 written on slips of paper. If you choose one slip at random, what is the probability that you will not select a number which divisible by 3?a. 1/3b. 2/3c. 5/8d. 3/8
Answers
24 is divisible by 3
21 is divisible by 3
18 is divisible by 3
15 is divisible by 3
12 is divisible by 3
9 is divisible by 3
6 is divisible by 3
3 is divisible by 3
8 numbers are divisible by 3
Total numbers: 24
24-8 = 16 numbers are not divisible by 3
Divide the number that are not divisible by 3 , by the total numbers:
16 /24 = 2/3
1455 is 150% of blank
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We have to calculate of which value x we have that 1455 is the 150%.
We have to express mathematically "150% of x is 1455". This can be written as:
[tex]\begin{gathered} \frac{150}{100}\cdot x=1455 \\ 1.5x=1455 \\ x=\frac{1455}{1.5} \\ x=970 \end{gathered}[/tex]Answer: 1455 is 150% of 970.
I have a triangle and diamond on an equation which is =1.05so I am asking am I suppose to divide by 2 to get the answer?
Answers
Let,
T = Triangle
S = Semi Circle
R = Star
D = Diamond
Given:
a.) 4 Triangles = 2 Semi Circle + 2 Star → 4T = 2S + 2R
b.) 1 Triangle + 1 Diamond = 1.05 → 1T + 1D = 1.05
c.) 1 Star + 1 Semi Circle = 0.525 → 1R + 1S = 0.525
d.) Diamond = ?
For us to be able to determine the value of the diamond, we must be able to determine the value of the Triangle.
For us to get it, we will be using first the equation at a and c.
4T = 2S + 2R
1R + 1S = 0.525
We get,
2S + 2R = 2(1S + 1R)
2S + 2R = 2(0.525)
2S + 2R = 1.05
Let's now get the value of the triangle,
4T = 2S + 2R
4T = 1.05
T = 1.05/4
T = 0.2625 (Value per triangle)
Let's now determine the value of the DIAMOND.
1 Triangle + 1 Diamond = 1.05 → 1T + 1D = 1.05
1T + 1D = 1.05
1(0.2625) + 1D = 1.05
0.2625 + 1D = 1.05
1D = 1.05 - 0.2625
1D = D = 0.7875
ANSWER: The value of the diamond is 0.7875